| File: | src/lib/libm/src/s_ctanl.c |
| Warning: | line 146, column 3 Value stored to 'd' is never read |
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| 1 | /* $OpenBSD: s_ctanl.c,v 1.3 2011/07/20 21:02:51 martynas Exp $ */ |
| 2 | |
| 3 | /* |
| 4 | * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net> |
| 5 | * |
| 6 | * Permission to use, copy, modify, and distribute this software for any |
| 7 | * purpose with or without fee is hereby granted, provided that the above |
| 8 | * copyright notice and this permission notice appear in all copies. |
| 9 | * |
| 10 | * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES |
| 11 | * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF |
| 12 | * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR |
| 13 | * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES |
| 14 | * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN |
| 15 | * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF |
| 16 | * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. |
| 17 | */ |
| 18 | |
| 19 | /* ctanl() |
| 20 | * |
| 21 | * Complex circular tangent |
| 22 | * |
| 23 | * |
| 24 | * |
| 25 | * SYNOPSIS: |
| 26 | * |
| 27 | * long double complex ctanl(); |
| 28 | * long double complex z, w; |
| 29 | * |
| 30 | * w = ctanl( z ); |
| 31 | * |
| 32 | * |
| 33 | * |
| 34 | * DESCRIPTION: |
| 35 | * |
| 36 | * If |
| 37 | * z = x + iy, |
| 38 | * |
| 39 | * then |
| 40 | * |
| 41 | * sin 2x + i sinh 2y |
| 42 | * w = --------------------. |
| 43 | * cos 2x + cosh 2y |
| 44 | * |
| 45 | * On the real axis the denominator is zero at odd multiples |
| 46 | * of PI/2. The denominator is evaluated by its Taylor |
| 47 | * series near these points. |
| 48 | * |
| 49 | * |
| 50 | * ACCURACY: |
| 51 | * |
| 52 | * Relative error: |
| 53 | * arithmetic domain # trials peak rms |
| 54 | * DEC -10,+10 5200 7.1e-17 1.6e-17 |
| 55 | * IEEE -10,+10 30000 7.2e-16 1.2e-16 |
| 56 | * Also tested by ctan * ccot = 1 and catan(ctan(z)) = z. |
| 57 | */ |
| 58 | |
| 59 | #include <complex_Complex.h> |
| 60 | #include <float.h> |
| 61 | #include <math.h> |
| 62 | |
| 63 | #if LDBL_MANT_DIG64 == 64 |
| 64 | static const long double MACHEPL= 5.42101086242752217003726400434970855712890625E-20L; |
| 65 | #elif LDBL_MANT_DIG64 == 113 |
| 66 | static const long double MACHEPL = 9.629649721936179265279889712924636592690508e-35L; |
| 67 | #endif |
| 68 | |
| 69 | static const long double PIL = 3.141592653589793238462643383279502884197169L; |
| 70 | static const long double DP1 = 3.14159265358979323829596852490908531763125L; |
| 71 | static const long double DP2 = 1.6667485837041756656403424829301998703007e-19L; |
| 72 | static const long double DP3 = 1.8830410776607851167459095484560349402753e-39L; |
| 73 | |
| 74 | static long double |
| 75 | redupil(long double x) |
| 76 | { |
| 77 | long double t; |
| 78 | long i; |
| 79 | |
| 80 | t = x / PIL; |
| 81 | if (t >= 0.0L) |
| 82 | t += 0.5L; |
| 83 | else |
| 84 | t -= 0.5L; |
| 85 | |
| 86 | i = t; /* the multiple */ |
| 87 | t = i; |
| 88 | t = ((x - t * DP1) - t * DP2) - t * DP3; |
| 89 | return (t); |
| 90 | } |
| 91 | |
| 92 | static long double |
| 93 | ctansl(long double complex_Complex z) |
| 94 | { |
| 95 | long double f, x, x2, y, y2, rn, t; |
| 96 | long double d; |
| 97 | |
| 98 | x = fabsl(2.0L * creall(z)); |
| 99 | y = fabsl(2.0L * cimagl(z)); |
| 100 | |
| 101 | x = redupil(x); |
| 102 | |
| 103 | x = x * x; |
| 104 | y = y * y; |
| 105 | x2 = 1.0L; |
| 106 | y2 = 1.0L; |
| 107 | f = 1.0L; |
| 108 | rn = 0.0L; |
| 109 | d = 0.0L; |
| 110 | do { |
| 111 | rn += 1.0L; |
| 112 | f *= rn; |
| 113 | rn += 1.0L; |
| 114 | f *= rn; |
| 115 | x2 *= x; |
| 116 | y2 *= y; |
| 117 | t = y2 + x2; |
| 118 | t /= f; |
| 119 | d += t; |
| 120 | |
| 121 | rn += 1.0L; |
| 122 | f *= rn; |
| 123 | rn += 1.0L; |
| 124 | f *= rn; |
| 125 | x2 *= x; |
| 126 | y2 *= y; |
| 127 | t = y2 - x2; |
| 128 | t /= f; |
| 129 | d += t; |
| 130 | } |
| 131 | while (fabsl(t/d) > MACHEPL); |
| 132 | return(d); |
| 133 | } |
| 134 | |
| 135 | long double complex_Complex |
| 136 | ctanl(long double complex_Complex z) |
| 137 | { |
| 138 | long double complex_Complex w; |
| 139 | long double d, x, y; |
| 140 | |
| 141 | x = creall(z); |
| 142 | y = cimagl(z); |
| 143 | d = cosl(2.0L * x) + coshl(2.0L * y); |
| 144 | |
| 145 | if (fabsl(d) < 0.25L) { |
| 146 | d = fabsl(d); |
Value stored to 'd' is never read | |
| 147 | d = ctansl(z); |
| 148 | } |
| 149 | if (d == 0.0L) { |
| 150 | /*mtherr( "ctan", OVERFLOW );*/ |
| 151 | w = LDBL_MAX1.18973149535723176502e+4932L + LDBL_MAX1.18973149535723176502e+4932L * I1.0fi; |
| 152 | return (w); |
| 153 | } |
| 154 | |
| 155 | w = sinl(2.0L * x) / d + (sinhl(2.0L * y) / d) * I1.0fi; |
| 156 | return (w); |
| 157 | } |